Year: 2006
Type: preprint
Abstract: We study cyclotomic association schemes over a finite commutative ring $R$ with identity. The main interest for us is to identify the normal cyclotomic schemes $C$, i.e. those for which $Aut(C)$ is a subgroup of the one-dimensional affine semilinear group over $R$. The problem is reduced to the case when the ring $R$ is local in which a necessary condition of normality in terms of the subgroup of $R^\times$ defining $C$, is given. This condition is proved to be sufficient for a class of local rings including the Galois rings of odd characteristic.
Source: arXiv (Cornell University)
Authors: Evdokimov, Sergei, Ponomarenko, Ilia
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950916488